The flexural rigidity of a rod-like structure like a microtubule is a measure of its bending stiffness.

Flexural rigidity is given by EL, where E is the Young?s modulus and L is the geometrical moment of

inertia of the rod cross-section. For a hollow cylindrical cylinder with outer diameter, , and inner

diameter, , the moment of inertia about an axis through the middle of its cross-section is

The flexural rigidity of microtubules can be measured in several ways.

Assuming the microtubule behaves like a slender rod of length L, the critical force, , at which buckling occurs is given by Euler?s formula:

Applying this equation, the flexural rigidity, EL, is estimated by measuring the force at which a

microtubule of known length is observed to buckle.

A)

Critical loads for 10 microtubules are shown in below. Calculate the flexural rigidity for each

microtubule and determine the mean flexural rigidity for all the microtubules tested.

B)

Use the mean flexural rigidity you calculated in (A) to estimate the Young?s modulus of a

microtubule. State your assumptions about the geometry of a microtubule. Assume that the inner and

outer diameters of the microtubule are 16nm and 24nm respectively.

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